Discuss the trajectory of a charged particle in a magnetic...

Name: Problem 6, Chapter 18: Essential College Physics
Uploaded: 2021-05-30T13:25:28-08:00
Duration: 1 min 37 s
Channel: Ajay Singhal
Description: Discuss the trajectory of a charged particle in a magnetic field when the particle's velocity is not perpendicular to the field. Explain why the motion is a helix, such that the particle's velocity component in the direction of the magnetic field is constant, and the motion in the perpendicular direction is circular.

Discuss the trajectory of a charged particle in a magnetic field when the particle's velocity is not perpendicular to the field. Explain why the motion is a helix, such that the particle's velocity component in the direction of the magnetic field is constant, and the motion in the perpendicular direction is circular.

Key Concepts

Circular Motion in a Magnetic Field

The component of the velocity that is perpendicular to the magnetic field experiences a force that is always directed towards the center of a circular path. This results in circular motion at a constant speed, where the magnetic force acts as the centripetal force necessary for circular motion.

Helical Motion

Helical motion arises from the combination of constant linear motion along the direction of the magnetic field and circular motion in the perpendicular plane. This superposition results in the particle tracing out a helix, where the pitch of the helix is determined by the constant velocity component along the field.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in a magnetic field, calculated as the cross product of the particle's velocity and the magnetic field. This force is always perpendicular to both the velocity of the particle and the magnetic field, causing the particle to change direction but not its speed when only magnetic forces are acting.

Decomposition of Velocity

When a charged particle's velocity is not completely perpendicular to the magnetic field, its velocity can be decomposed into two components: one parallel to the field and one perpendicular. The parallel component remains unaffected by the magnetic force, allowing it to persist unchanged, while the perpendicular component is acted upon by the magnetic force.

Transcript

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